To simplify the expression \( 7^{-2} \cdot 7^{7} \), we can use the property of exponents that states when multiplying with the same base, we add the exponents.
Here's how to do it:
\[ 7^{-2} \cdot 7^{7} = 7^{-2 + 7} = 7^{5} \]
Thus, the simplified expression is:
\[ 7^5 \]
If you need the numerical value of \( 7^5 \):
\[ 7^5 = 7 \times 7 \times 7 \times 7 \times 7 = 16807 \]
So, the final simplified result is:
\[ 7^5 \text{ or } 16807 \]